4.4 Excitation-Emission Transition Dipole Imaging
4.4.1 Experimental Setup and Methods
Figure 4.38 shows a schematic representation of the optical setup used here. A pulsed white light laser (Fianium SC400-4-80) together with an acousto-optic tunable filter (AOTFnC-400.650-TN) was used for excitation (λexc= 640 nm). The linearly polar-ized TEM00 beam was then passed through a pixelated liquid crystal mode converter
4.4. EXC-EM TDM CHAPTER 4. SM ORIENTATION
Figure 4.38: Experimental setup showing the path of the excitation beam in yellow and the fluo-rescence emission pathways as red. The collimated (TEM00) pulsed laser is passed through a linear polarizer (LP). Any unwanted wavelengths present were blocked using a clean up filter (CL) before the beam was passed through the mode converter. Thereafter, the beam was mode cleaned by focusing through a pinhole (PH) leading to a doughnut profile radially polarized laser. The beamsplitter (BS) reflects the laser into the objective which focuses the light onto the sample. The inset shows the calcu-lated longitudinal and the transverse electric field components on the surface of the substrate 0.5µm around the optical axis (scalebar = 200 nm) The sample is scanned first by focusing the photons onto a single photon avalanche photodetector (SPAD), to obtain the excitation image and the positions of the emitters. Later, a replaceable mirror is placed to reflect the emission photons onto an EMCCD camera shifted from the imaging plane, and a defocused image at each position is captured. [This figure has been published in the article [151].]
(Arcoptix S.A.) which rotates the light polarization spatially to generate a radially po-larized TM01 beam. This beam was then focused on the surface of a sample through a high N.A. objective lens (APON 60X OTIRF, N.A. = 1.49, Olympus) after reflect-ing on a 30 R : 70 T non-polarizreflect-ing beam splitter (ThorLabs BS019). The sample was prepared by spin-coating 10µL of 1 nM Atto 655 (AttoTech, GmbH) dye solution on top of a cleaned glass (nref = 1.52) coverslip and then scanned using a piezoelec-tric stage with a pixel size of 50 nm. Collected photons were focused onto the active area of a single-photon avalanche photodiode (τ-SPAD, PicoQuant) and counted with a multichannel picosecond event timer (HydraHarp 400, PicoQuant). The backscattered
CHAPTER 4. SM ORIENTATION 4.4. EXC-EM TDM
excitation light was blocked using a long pass filter (BLP01-635R, Semrock BrightLine) and additional band pass filters (Semrock BrightLine FF01-692/40). The laser power,
∼4 kW/cm2, and the sample scanning rate, 3 ms per pixel were chosen optimally so as to minimize photobleaching of the dye molecules and achieve a reasonable signal-to-noise ratio in the excitation images. Thereafter, the piezo stage was parked on each molecule’s position, identified from the scan image, and the fluorescence collected was guided with the help of a replaceable mirror onto an EMCCD camera (iXon DU860-D, Andor Technology). For the chosen magnification, the pixel size of the camera corre-sponds to 60 nm×60 nm area in the object space. The camera was shifted from the image plane by aboutδz= 0.9µm above the focal plane in the object space. Each image was acquired with an exposure of 9 s, an electron multiplying gain of 100, and with the excitation power of∼10 kW/cm2. All the data collection and hardware synchronization was performed on a custom written LabVIEW platform.
As a second system, we investigated molecules of the dye Alexa 488 (Invitrogen) embedded into a thin layer of polymer by spin-coating a 0.1% w/v PVA/water (refractive index 1.55) solution containing 1 nM of the dye on top of a cleaned coverslip at 6000 rpm for 60 seconds, yielding a distribution of immobilized single molecules within a thin polymer film. The sample was excited with an excitation power of 1.6 kW/cm2 at 485 nm and a dwell time per pixel same as the previous measurements. As before, backscattered excitation light was blocked using suitable long (BLP01-488R, Semrock) and band pass (FF02-525/40, Semrock) filters. The defocused images were obtained at the same excitation power but with the camera set to a position such that the effective defocusing at the object spaceδzwas around 0.6µm, and the acquisition time was now 15 s.
4.4.2 Results
Measurements on Single Molecules
The first row in figure 4.39 shows 5 out of 131 excitation patterns of the Atto 655 molecules acquired during the scans. The peak count rates observed for these molecules range between 17 to 30 kHz in the focus of excitation and the total number of photons collected between 1×103 to 4.5×103. We estimated the excited-state decay lifetime (τf) for each molecule individually after pattern matching. Theτf values show a distri-bution peaked around 2.84 ns. The third row in figure 4.39 shows the defocused images corresponding to the excitation patterns shown in the first row. We estimated the num-ber of photons in each pixel by converting the counts into photon numnum-bers, taking into account the electron-multiplying gain used and the sensitivity of the camera. This was done by first subtracting the camera bias from the recorded camera counts, multiplying the resultant with the sensitivity (average number of photons required to produce one
4.4. EXC-EM TDM CHAPTER 4. SM ORIENTATION
Figure 4.39: Emission and excitation patterns of five Atto 655 molecules. The top row shows the excitation images, the second row the corresponding fitted patterns, the third row shows the defocused images, and the fourth row the fitted emission patterns. The scan pixel size is 50 nm and each excitation image is 25 ×25 pixels; whereas the camera pixel size is∼60 nm with each defocused image spanning over 40 × 40 pixels. The last row is a depiction of both the excitation (light) and emission (dark) dipole orientations, as fitted from the measurements. Theαand theβ values indicate the orientation with respect to the z- and x-axes, shown for the first molecule. [This figure has been published in the article [151].] The fitted orientation angles for both dipoles are:
Molecule # βexc αexc βem αem
1 61.2◦ 83.2◦ 86.6◦ 76.4◦
2 101.6◦ 89.2◦ 288.8◦ 87.9◦
3 124.5◦ 83.1◦ 315.9◦ 87◦
4 356.9◦ 88.6◦ 162.7◦ 83.8◦
5 87.5◦ 7.92◦ 82.2◦ 88.1◦
count, which depends on the pre-amp setting and the read-out rate), and finally divid-ing it by the electron gain used. The total number of photons detected per molecule determined in this way range between 1.6×105 to 1.2×106.
For data evaluation, we first performed the least-squares minimization pattern match-ing that we described in section 4.1.4 for both excitation and emission intensity patterns.
The obtained fit parameters served as the initial guess values for the optimization of a log-likelihood function assuming Poissonian statistics [143]
L=−X
r
[I(r)·log(A·P(r|rP, β, α) +B)−(A·P(r|rP, β, α) +B)] (4.32)
CHAPTER 4. SM ORIENTATION 4.4. EXC-EM TDM
Figure 4.40: The left column shows the raw data cropped from scan images acquired using a radially polarized laser for three molecules. The right column shows the patterns identified using the least-squares minimization pattern match algorithm; whereas the middle column shows the refinement of the parameters using the described maximum likelihood estimation (MLE).
Molecule # MLE (β, α) Pattern Match (β, α) 1 (340.0◦,80.3◦) (339◦,75◦) 2 (118.8◦,83.2◦) (115◦,90◦) 3 (176.3◦,88.3◦) (175◦,90◦)
which yields refined parameters beyond the discrete set of values recovered by the pat-tern matching. Here,I(r) denotes the measured image andP(r|rP, β, α) is the pattern calculated using the wave-optical model described in section 4.3.1. The optimization was done for the parameters rP, β, α, A, B, where rP is the pattern’s central location, A is the integrated intensity, and B the background intensity value. The optimization algorithm was based on a conjugate gradient method. Refinement of the fit using the log-likelihood function increases the fit accuracy by five to ten-fold. Theoretically, one could use, for the pattern matching, a set of patterns with a ten-fold finer angular spac-ing ofα- andβ-values, which would make the log likelihood-based refinement obsolete.
However, such an approach would be computationally prohibitive.
The second and fourth rows of figure 4.39 show the fitted excitation and emission patterns for five Atto 655 molecules. In order to estimate the fitting errors, we applied a bootstrap algorithm where new noisy samples were generated based on the estimated
4.4. EXC-EM TDM CHAPTER 4. SM ORIENTATION
parameters, and then fitted again. In this way, a distribution for each parameter was obtained using the above maximum likelihood estimator by fitting one thousand re-sampled images. Theα-values for almost all molecules were close to 90◦, which indicates that the spin-coated molecules were lying mostly flat on the substrate consistent with what we saw in our previous work in section 3.2.2. The standard errors of α and β for the orientation of pexc were both smaller than 2◦, whereas for the orientation of pem, they were both smaller than 0.4◦. These small values of the standard deviations for the obtained angles are due to the high number of total detected photons per molecule.
Figure 4.41 shows the result of bootstrapping for the estimation of the orientations of both the TDMs of a molecule. Further, the small values of the standard deviations for
Figure 4.41: Bootstrap results showing the distribution of the orientations for an Atto 655 molecule.
The number of photons collected during the scanning was∼ 3.2×103 whereas∼ 2.4×105 on the defocused camera for the emission pattern. The standard deviations of β and αfrom the bootstrap data of the excitation pattern are 1.6◦ and 1.5◦; whereas for the emission pattern they are 0.5◦ and 0.4◦.
the angles obtained using the bootstrap method described above establishes the accuracy of the fitting method for the model intensity patterns calculated with the number of photons and the background values estimated from the fitting itself. The quality of the defocused images is sensitive to small obstructions or any undesired tilt present in the emission pathways, which are hard to rectify in a custom built setup that lead to slightly asymmetric defocused images. This does not, however, affect the estimation of the in-plane angles β, but introduces small systematic errors in the estimation of the out-of-plane angles α of the pem, affecting slightly the accuracy of the fitted results.
CHAPTER 4. SM ORIENTATION 4.4. EXC-EM TDM
Figure 4.42: Distributions of determinedγ values (left) and their corresponding distribution (right) for 25 molecules Atto 655 molecules on a glass surface (blue), and for 49 Alexa 488 molecules embedded into a polymer film (red). The error bars shown in the left figure were estimating using a bootstrapping algorithm. The right side shows the probability distributions with a bin width of 5◦. The distributions were fitted with a Poisson distribution (solid lines) yielding a mean value ofγ equal to 14.6◦ for Atto 655 and equal to 22.5◦ for Alexa 488. The results for the first five molecules of Atto 655 correspond to the the five measurements shown in figure 4.39 and listed in table beneath. [This figure has been published in the article [151].]
The total number of photons collected from the Alexa 488 molecules ranged between 2×104 and 1.5×105 on the defocused camera, and between 0.7×103 and 3.4×103 in the excitation images. Now, the determined α-values showed a broad distribution between 0◦ and 90◦ indicating that the molecules immobilized within the polymer layer did not have a preferred orientation parallel to the surface, in contrast to the Atto 655 sample. The standard errors ofα and β for pexc were around 5◦, whereas for pem they were around 1◦. The difference in precision between the Atto 655 and the Alexa 488 measurements can be explained by (i) the fewer number of total photons that were collected from the Alexa 488 dye molecules; and (ii) the smaller defocusing value chosen in order to achieve a good signal-to-noise ratio, which affects the accuracy of estimating the α and β values, in particular, for dipoles oriented almost vertically.
After obtaining the orientations of both pexc and pem, it is now straightforward to estimate the inclination angle γ between excitation and emission dipoles for each molecule. Figure 4.42 shows the distribution of γ for 25 measured Atto 655 molecules and for 49 Alexa 488 molecules. The values for γ vary between 7◦ and 33◦ with a mean of ∼ 15◦ for Atto 655 molecules, whereas a larger mean value of ∼ 23◦ and
4.4. EXC-EM TDM CHAPTER 4. SM ORIENTATION
broader distribution for the Alexa 488 molecules. This shows that there is a significant variation of the transition dipoles during the excitation and emission processes for both the species.
Ensemble Anisotropy Measurements
In order to compare the obtained values with an ensemble estimate for the γ values, we performed time-resolved anisotropy measurements on ∼ 1µM in 90% glycerol solu-tions of the two dyes. The anisotropy measurements were performed by focusing two orthogonally polarized lasers of the same excitation wavelength through a low numerical aperture (UPlanSApo 20x, N.A. = 0.75, Olympus) air objective. A low N.A. objective is essential for such measurements in order to reduce the depolarization of the excitation laser in the focus. For the excitation of Atto 655 molecules, we used two 640 nm diode lasers (LDH-D-C-640, PicoQuant) with a pulse width of 100 ps, pulsed alternatively with a repetition rate of 40 MHz each with the help of a multichannel picosecond diode laser driver (PDL 828 ‘Sepia II’, PicoQuant). This gives a time delay of 12.5 ns between the two alternate polarization pulses in the focus. Clean-up filters (Z640/10X, Chroma Technology) were used to block any unwanted wavelength from the lasers. The power of each laser was set to 0.1 kW/cm2. The high concentration ensured the presence of all possible orientations of the excitation and emission transition dipoles. The emission collected through the same objective was focused onto a 50µm pinhole and thereafter split and refocused onto the active area (180µm) of two Single Photon Counting Mod-ules (SPCM CD, Excelitas Technologies Inc., timing resolution 350 ps) by a polarizing beamsplitter cube. The emission light was filtered from any background or scattering by passing through band-pass filters (BrightLine HC 692/40, Semrock) in front of the de-tectors. The detected photons were recorded with 8 ps time resolution by a multichannel picosecond event timer and TCSPC module (HydraHarp 400, PicoQuant). In such an experimental setup, each detector measures two consecutive fluorescence decay curves within one complete excitation cycle, one corresponding to the laser which is parallel in polarization to the detector (higher amplitude) and the other which is orthogonal to it (lower amplitude). The four TCSPC curves thus recorded can be named as Ik,k,Ik,⊥, I⊥,k,I⊥,⊥ where the first symbol represents the polarization of the laser with respect to a fixed k and ⊥ orientation in the laboratory reference frame and the second symbol marks the orientation for the detection. The time resolved anisotropyr(τ) is calculated from the following equation:
CHAPTER 4. SM ORIENTATION 4.4. EXC-EM TDM
where τ is the time delay between the laser pulse and tcspc channel. Here, τ is deter-mined separately for each TCSPC curve. The time channel corresponding to roughly half the maximum counts on the rising edge of the TCSPC curve was identified ashτ0i.
An exponential tail fitting is performed on r(τ) and the rotational diffusion D of the dye molecules is obtained. Thereafter, ther0 for Atto 655 was obtained by extrapolat-ing the fitted curve to time τ0. This corresponds to the ensemble average of the angle between the excitation and the emission dipoleshγi values, which is given by (see also reference [83]):
hγi= cos−1
r5r0+ 1
3 , 06γ 6 π
2 (4.34)
Similarly, the measurements for Alexa 488 were performed using two orthogonally polar-ized 485 nm (LDH-P-C-485B) lasers, appropriate clean-up filters (F49-488, AHF) before them, and band-pass filters (FF01-525/30) in the detection.
We obtained r0 = 0.361 and 0.33 for the Atto 655 and Alexa 488 measurements, which that correspond tohγi values of 14.9◦ and 19.9◦ respectively using equation 4.34.
These are values are in good agreement to the mean values from the single-molecule data presented above.
4.4.3 Discussion and Outlook
The important message that is conveyed from these measurements is that significant reorganization in the structure of the molecules after the excitation takes place which leads to an overall change in the electron density over the structures before the emission takes place. This shows up as non-negligible hγi. One can model the electron density maps of the molecule’s structure in the excited and ground vibrational states in the HOMO and LUMO electronic states, similar to the calculations shown in [147], in order to compare the obtained values with the theoretical calculations (beyond the scope of this thesis). It is beyond the scope of our work to account for the wide variations inγ that we observe for individual molecules. We, however, speculate that the bending of the molecule’s backbone structure, depending on the extent of local electrostatic and van der Waals interactions with the substrate can be a key reason. Correlating the values of γ together with the force of binding with the interface, measured using single-molecule force sensitive techniques might be useful to investigate the local surface effects [152].
The method we present here can be extended to the imaging of magnetic dipoles, electric multipoles, and quantum dots, and probe their behavior in different electro-magnetic environments. Quantum dots, as we saw in the previous section, have a 2D degenerate emission transition dipole located in a plane perpendicular to their crys-talline c-axis [27]. Theoretical calculations and a few experimental results show that
4.4. EXC-EM TDM CHAPTER 4. SM ORIENTATION
when placed close to metallic nanostructures or optical antennas, the degeneracy is lifted off and they show polarized emission properties similar to a dipole [13, 28]. A complete behavior of the transitions properties can only be studied by monitoring both, the excitation and emission transition dipole imaging simultaneously.
One can try various combinations of methods that determine the excitation and emission transition dipoles of molecules, such as, the combination of radially polar-ized excitation scanning together with a detection scheme as was employed in work of Hohlbein et al. by splitting the emitted photons onto three single photon count-ing detectors is much suited for rapidly measurcount-ing the orientations of both transitions dipoles of single molecules [62]. By comparing the intensity ratios on the detectors, one can determine, using simple relations, the in-plane and out-of-plane orientations for the emission transition dipole of a single chromophore. In this way, one has all the information, including the fluorescence lifetime of each molecule, just while acquiring a scan image. In comparison to the method we adopted for the study above, this method is faster (up to an order of magnitude) and can achieve a higher throughput, since one need not collect a high number of photons for the emission as we require. However, the significant advantage of using defocused imaging for the determination of the emission transition probabilities, over most existing techniques, is its ability to distinguish be-tween a single dipole emitter and a multidimensional or isotropic emitter. The structural details of the emission from exotic emitters, such as quantum dots for example, can be resolved and investigated easily by using this method. By introducing a beamsplitter in place of a mirror, such that only 70% of the light is used for defocused imaging, the remaining fraction of the detected photons can be used used for fluorescence lifetime estimation, for studying the photophysics of the emitter, and even photon antibunching studies if the emission center is stable enough. This information can be highly useful when studying the photoluminescence properties of such exotic emitters.
Together with the orientation information, one obtains the lateral position of an emitter in the object space. Due to the high number of photons collected on the camera, the precision of position determination, or localization precision, can go down to a few nanometers. From the bootstrapping results of the data presented above, we achieve 2 to 3 nm lateral localization precision indeed. This means, if combined with smMIET technique, one has all the information, i.e. fluorescence lifetimes, emission transition dipole orientations for obtaining the axial distances, and defocused intensity patterns to localize the molecules laterally. Thereby, one can localize individual emitters in all three dimensions, with nanometer precision. It must again be pointed out here that the lateral position obtained from such an analysis already takes into account the asymmetric angular emission distribution from a fixed dipole, and therefore, is free of any orientation artifacts.